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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

The modulus of the boundary values of bounded analytic functions of several variables


Author: Chester Alan Jacewicz
Journal: Trans. Amer. Math. Soc. 176 (1973), 253-261
MSC: Primary 32A10
DOI: https://doi.org/10.1090/S0002-9947-1973-0311931-3
MathSciNet review: 0311931
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Abstract: One necessary condition and one sufficient condition are given in order that a nonnegative function be the modulus of the boundary values of a bounded analytic function on the polydisc. As a consequence, a weak version of a theorem of F. Riesz is generalized to several variables. For special classes of functions several conditions are given which are equivalent to a function's being the modulus of the boundary values of a bounded analytic function. Finally, an algebraic structure is provided for these special classes of functions.


References [Enhancements On Off] (What's this?)

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  • [2] W. Rudin, Function theory in polydiscs, Benjamin, New York, 1969. MR 41 #501. MR 0255841 (41:501)
  • [3] -, Fourier analysis on groups, Interscience Tracts in Pure and Appl. Math., no. 12, Interscience, New York, 1962. MR 27 #2808. MR 0152834 (27:2808)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1973-0311931-3
Keywords: Hardy spaces, bounded analytic functions, boundary values, boundary modulus
Article copyright: © Copyright 1973 American Mathematical Society

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